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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 402930q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402930.q4 | 402930q1 | \([1, -1, 0, 590760, -2136138944]\) | \(17655210697319/1536373555200\) | \(-1984177234959453388800\) | \([2]\) | \(20643840\) | \(2.7661\) | \(\Gamma_0(N)\)-optimal* |
402930.q3 | 402930q2 | \([1, -1, 0, -21711960, -37593003200]\) | \(876470240549871001/34348976640000\) | \(44360603098489244160000\) | \([2, 2]\) | \(41287680\) | \(3.1127\) | \(\Gamma_0(N)\)-optimal* |
402930.q2 | 402930q3 | \([1, -1, 0, -56211480, 111576021376]\) | \(15209507008787085721/4638548475000000\) | \(5990536778116297275000000\) | \([2]\) | \(82575360\) | \(3.4593\) | \(\Gamma_0(N)\)-optimal* |
402930.q1 | 402930q4 | \([1, -1, 0, -344055960, -2456268972800]\) | \(3487605307056720495001/5686728379200\) | \(7344227550140085844800\) | \([2]\) | \(82575360\) | \(3.4593\) |
Rank
sage: E.rank()
The elliptic curves in class 402930q have rank \(0\).
Complex multiplication
The elliptic curves in class 402930q do not have complex multiplication.Modular form 402930.2.a.q
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.